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 A253597 Least Lucas-Carmichael number divisible by the n-th prime. 3
 399, 935, 399, 935, 2015, 935, 399, 4991, 51359, 2015, 1584599, 20705, 5719, 18095, 2915, 46079, 162687, 22847, 46079, 16719263, 12719, 7055, 80189, 104663, 20705, 482143, 196559, 60059, 90287, 162687, 3441239, 13971671 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Has any odd prime number at least one Lucas-Carmichael multiple? LINKS Tim Johannes Ohrtmann and Charles R Greathouse IV, Table of n, a(n) for n = 2..1000 (terms up to 202 from Ohrtmann) FORMULA a(n) >> n^2 log^2 n. - Charles R Greathouse IV, Feb 03 2015 EXAMPLE a(2) = 399 because this is the least Lucas-Carmichael number which is divisible by 3 (the second prime number). MATHEMATICA LucasCarmichaelQ[n_] := Block[{fi = FactorInteger@ n}, !PrimeQ@ n && Times @@ (Last@# & /@ fi) == 1 && Plus @@ Mod[n + 1, 1 + First@# & /@ fi] == 0]; f[n_] := Block[{k = p = Prime@ n}, While[ !LucasCarmichaelQ@ k, k += p]; k]; Array[f, 35, 2] (* Robert G. Wilson v, Feb 11 2015 *) PROG (PARI) is_A006972(n)=my(f=factor(n)); for(i=1, #f[, 1], if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f[, 1]>1 a(n) = pn = prime(n); ln = 1; until (is_A006972(ln) && (ln % pn == 0), ln++); ln; (PARI) is_A006972(n)=my(f=factor(n)); for(i=1, #f~, if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f~>1 a(n)=my(p=prime(n), c=p^2+p, t=p); while(!is_A006972(t+=c), ); t \\ Charles R Greathouse IV, Feb 03 2015 CROSSREFS Cf. A006972, A065091, A253598. Sequence in context: A126231 A158317 A227008 * A006972 A216925 A292573 Adjacent sequences: A253594 A253595 A253596 * A253598 A253599 A253600 KEYWORD nonn AUTHOR Tim Johannes Ohrtmann, Jan 05 2015 STATUS approved

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Last modified May 21 13:39 EDT 2024. Contains 372736 sequences. (Running on oeis4.)